Another possible root for noel, also from the French, is the word nouvelles, meaning news. As the popular carol says, The first noel the angels did say / Was to certain poor shepherds. . . . The meaning of news certainly makes sense in that context; however, the early usage and definition of noel seem to focus more on the idea of birth, and that is probably the more accurate meaning. (https://www.gotquestions.org/Noel-meaning.html)
You can redefine it however you see fit.
I see that word differently.